Spectral invariants: Difference between revisions

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'''Bose-Einstein condensation of excitons'''. In contrast to [[electron]]s and [[electron hole]]s which are [[fermions]], their combination to [[excitons]] renders these [[bosons]] as it was first proposed for [[helium-4]] to explain its observed [[superfluidity]]<ref>London, F (1938) The <math>\lambda</math>-Point of Liquid Helium and the Bose-Einstein Condensation, Nature, '''141''', 3571</ref> at the <math>\lambda</math>-point (2,17K) of [[liquid helium]].<ref>Einstein, A. (1920) Proc. Berlin Acad. Science</ref> This condensation occurs when all atomic particles fall into the same, lowest quantum state.<ref>Kapiza, P. Natur (1938) Nature '''141''' 3558</ref> Excitons should therefore also condensate, as proposed by Böer and colleagues in 1961,<ref>Blatt, J.M., K.W. Boer, and W. Brandt, (1962) Bose-Einstein Condensation of excitons, Phys. Rev. '''126.5''', 1691</ref> assuming a separate thermodynamic phase when the main distance between the excitons reaches the [[de Broglie wavelength]] <math>\lambda_{dB}</math>:
 
{{NumBlk|:|<math>n^{1/3} = \lambda_{dB} = \hbar (m_{\mathit{eff}}kT_{cr})^{-1/2}</math>|{{EquationRef|1}}}}
 
or estimating the critical temperature Tcr for exciton condensation as
{{NumBlk|:|<math>T_{cr} = n^{3/2}\hbar^{2} / km_{\mathit{eff}}</math>|{{EquationRef|2}}}}
with
{{NumBlk|:|<math>n = g\tau</math>.|{{EquationRef|3}}}}
 
Here <math>n</math> is the density of excitons, <math>m_{\mathit{eff}}</math> their effective mass, and <math>g</math> the optical generation rate of excitons, <math>\hbar = h/2\pi</math>, and <math>k</math> the conventional Planck and Boltzmann constant.
When entering the values of the tabulated constants <math>\hbar = 1.0547 \times 10^{-34}(Ws^2)</math>; {{pad|.5em}} <math>k = 1.381 \times 10^{-23}(Ws/K)</math> and assuming the exciton mass of the order of the electron mass
<math>m_{\mathit{eff}} = 9 \times 10^{-35} (Wcm^{3}s^{-2})</math> one estimates from ({{EquationNote|2}}) and ({{EquationNote|3}})
<math>T_{cr} = (g\tau)^{3/2}\hbar^{2}/(k m_{\mathit{eff}}) = (g\tau)^{3/2} \times 10^{-11}</math>
that means that for a critical temperature of <math>0.01K</math> one needs <math>g\tau = 10^6</math> that can be achieved with a reasonable generation rate of <math>10^5</math> by pumping with a tunable laser at the exciton wavelength, and a life time of 10 seconds in an ultrapure single crystal of <math>Cu_{2}0</math>.<ref>Aurora, C.P. (2001) Thermodynamics, McGraw-Hill</ref>
 
Condensate excitons are [[superfluid]] and will not show any interaction with phonons while the normal exciton absorption is broadened by phonons, in a superfluid, this interaction disappears and the optical absorption degenerates to a line. An experimental observation must await better equipment to reach lower temperatures and tunable lasers that can be used for pumping.
More detailed calculations were proposed by J. Keldysh<ref>Keldysh, L.V. (1964) Eksp. Teor. Fiz. '''47''', 1515; (1965) Sov. JEPT '''20''', 1018</ref> and later by [[David Snoke|D. Snoke et al]]<ref>Snoke D.W., Wolfe, J.P. and Mysyrovicz, A. (1990) Phys. Rev. B '''41''', 11171</ref> starting a large number of experimental verifications.<ref>Naka, N. and Nakasawa, N. (2005) J, Lumin. '''112''', 11</ref><ref>Joshioka, K., Ideguchi, T., Mysyrovicz, A and Kuwata-Gonokami, M. (2010) Phys. Rev B '''82''', 041201 (R)</ref><ref>Stolz H. and Semkat D. (2010) Phys. Rev. B '''81''', 081302 (R)</ref>
 
==See also==
* [[Bose–Einstein condensate]]
 
==References==
{{reflist}}
 
[[Category:Condensed matter physics]]

Latest revision as of 23:45, 29 March 2014

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Stop Throwing Away your hard earn cash on rental to landlord! Come seek for an awesome worth among the many least expensive PropertyCondominiumHouses at Singapore New Launch. I am an expert in Singapore actual estate, and I can help you to decide on the "right" property in Singapore - whether or not you are an experienced investor, a first time purchaser or a foreigner looking to transfer into Singapore. My companies cover you thru the whole process - discovering the property, negotiating the most effective worth, making a suggestion and closing the deal.I am here that will help you in every little thing to make the perfect actual property choice in your life. Nathan Suites, River Valley Singapore. PRIME Launch Please Call +65 8181-7777 Market your Singapore Property Actual Property 24-Hr On-line ON A REGULAR BASIS!! Condominium

Check out our characteristic properties for a list of condominium for lease with pictures and value. Feature Landed Home for Sale Feature Landed Home for Rent If you're or have been attempting to on the lookout for an inexpensive and low cost propertycondominiumhouse in Singapore however failed, check out our comprehensive low cost propertycondominiumhouse data beneath $1 million and we hope to have the opportunity to offer you our best service to your home search. Property Sort Any Rental Studio Residence Soho Units TownHouse Cluster Homes Landed Houses Terrace House Bungalow Serviced Residences Conservation House Shop House Warehouse Factory Resort Identification of the property supplied on the market Semi-furnished condominium on the market # 463 sf Open For Sale Now. Name 61000280

Complete the Sale - it is a technical term referring the cost of the contracted sale value (from you because the Buyer) in trade for the signed conveyance of title referred to as the "Instrument of Transfer" which effectively transfers the ownership of the property from the present owners to your self (as the brand new proprietor). Procedures for Buy 1.2. The Woodgrove is a small rental reverse The Woodgrove Condo. The biggest unit has a flooring space of 1410 sq. ft and this will not suit American households. Stunning new cluster homes in non-public landed property with high end fittings & finishes. 5 bedrooms of which three are ensuite + non-public house carry + 2 car heaps. Launching for sale. See Belgravia Villas view all property listings Anderson Property Consultants Rooms for Hire

Jun 14 River Valley Expat Alternative Residence for lease $4200 / 3br - 1250ft² - (Jervois Highway) pic real property - by dealer Jun 14 Hdb 3i Blk 535 Bedok North Road three For Sale @ $300,000 $300000 / 2br - 646ft² - (Bedok North Avenue three) pic actual property - by dealer Fri 13 Jun Jun thirteen Property ec in singapore (why not look here) s p ring street 2 & 3 bhk flat at s p ring highway (s p ring road) actual property - by owner Jun 10 BUGIS MRT, ROCHOR, IT MALL RETAIL OUTLET AT SIM LIM SQUARE FOR SALE $1300000 / 409ft² - (ROCHOR, BUGIS MRT) pic real estate - by broker Mon 09 Jun The Library - A Collection of Exclusive1 and a pair of bed room flats Why is the apartment named "The Library"? Manyinternational traders looking to London property as a secure haven Residential 100% BOUGHT. Business previous few items Renting a HDB flat

There are various methods I will help you discover and purchase or lease your dream property successfully. I view the buying / renting course of as a critical partnership which entails dedication and communication. To assist me understand and cater to your wants, tell me more about your self and what you're on the lookout for in my ( Shopping for or Renting ) Enquiries kinds. n prime of that, now you can access to my Singapore Multiple Itemizing Service - MLS data (similar to every other Singapore real property brokers do) so as to search for your dream properties online yourself that fit your necessities. And if you are looking at projects which are specialised by me, you'll be able to click on on at " My Tasks" info buttons.

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